Question

A sum of $5,000 is invested for five years with varying annual interest rates of 9%, 8%, 12%, 6%, and 15%, respectively (for example, in the first year 9% interest is accrued and 8% in the second year and so on). The future amount after 5 years is equal to ____________.

Answer 1

The future amount after 5 years is equal to $8,036.04.

Step-by-step explanation:

This can be calculated using the future value (FV) formula as follows:

FV after 1 year = Invested amount * (100% + Year 1 interest rate)^Number of year = $5,000 * (100% + 9%)^1 = $5,450.00

FV after 2 years = FV after 1 year * (100% + Year 2 interest rate)^Number of year = $5,450 * (100% + 8%)^1 = $5,886.00

FV after 3 years = FV after 2 years * (100% + Year 3 interest rate)^Number of year = $5,886 * (100% + 12%)^1 = $6,592.32

FV after 4 years = FV after 3 years * (100% + Year 4 interest rate)^Number of year = $6,592.32 * (100% + 6%)^1 = $6,987.86

FV after 5 years = FV after 4 years * (100% + Year 5 interest rate)^Number of year = $6,987.86 * (100% + 15%)^1 = $8,036.04

Therefore, the future amount after 5 years is equal to $8,036.04.

Note: The number of year used in each of the calculation above is 1 because the interest was changing after one year.